Soft-decision decoding is widely used within digital communications due to the performance gains which result from considering channel information within the decoding process. In order to realize the entire available gain, accurate information about a channel, or a signal transmitted, must be available to the receiver. However, since the structure of the channel is typically unknown, the channel parameters required to realize the entire available gain must be estimated by the receiver.
For an arbitrary binary communication channel with time-varying channel gain and noise variance, the channel can be modeled as: EQU r=p.sub.o x.sub.s +n (1)
where r is the received signal vector, p.sub.o is the channel gain (diagonal) matrix, x.sub.s is the transmitted signal vector, and n is is noise vector. Typically, a maximum likelihood decoder attempts to find the value of s, where s is some sequence, for which the probability density function of the vector (given that x.sub.s was transmitted) is largest. At this point, the maximum likelihood decoder declares that x.sub.s was the transmitted message.
Since the probability density function of the vector r is a function of both the channel gain and the noise variance, it is apparent that an accurate estimate of both the channel gain and the noise variance is required if valid soft-decision information is to be determined. However, the validity of the estimates of the channel gain and the noise variance is directly related to the accuracy of the estimates of the variance of the received signal power, .sigma..sub.r.sup.2 (k), and the variance of the received error signal, .sigma..sub.e.sup.2 (k), with respect to transmitted signal x.sub.s (k). While .sigma..sub.r.sup.2 (k) is simply related to the received signal power, .sigma..sub.e.sup.2 (k) is not as easy to obtain since, at the receiver, the transmitted sequence x.sub.s (k) is not available. Current techniques attempt to circumvent this problem by assuming that for a specific symbol in the received sequence of the signal, the error signal is the difference between the received signal and the closest constellation point (CCP). While this technique is adequate if the CCP corresponds to the transmitted signal, in cases where it does not (i.e., the channel has caused an error), the estimate of .sigma..sub.e.sup.2 (k) can be highly inaccurate.
Thus, a need exists for a new method and apparatus for estimating the variance of the received error signal .sigma..sub.e.sup.2 (k) which provides a significant increase in accuracy by fully utilizing the information available at the receiver.